Here is a potential starting point:
Rosewill REDBONE U3 Black SECC Steel USB 3.0, eSATA, 3x 120mm Fans Mid Tower Computer Case
Model #:REDBONE U3
Item #:N82E16811147160
Mail in Rebate Card
$59.99 -$10.00 Instant $49.99
The rebate brings this down to $40. It appears to be weak on cable management features, but I've been happy with all the Rosewill cases I've bought.
ASRock 990FX Extreme3 AM3+ AMD 990FX SATA 6Gb/s USB 3.0 ATX AMD Motherboard with UEFI BIOS
Model #:990FX Extreme3
Item #:N82E16813157281
$119.99 -$10.00 Instant $109.99
Should be a solid overclocker, and more future resistant than some of the 970 boards. Feel free to step back to a better 970 though, to shave the cost.
XFX Core Edition FX-785A-ZNL4 Radeon HD 7850 1GB 256-Bit GDDR5 PCI Express 3.0 x16 HDCP Ready CrossFireX Support Video Card
Model #:FX-785A-ZNL4
Item #:N82E16814150642
Mail in Rebate Card
$169.99 $169.99
Pretty good bang/buck.
Antec EarthWatts Green EA-380D Green 380W Continuous power ATX12V v2.3 / EPS12V 80 PLUS BRONZE Certified Active PFC Power ...
Model #:EA-380D Green
Item #:N82E16817371033
$59.99 -$15.00 Instant $44.99
Solid budget PSU; can run any card with a single PCIe power cable.
AMD FX-6300 Vishera 3.5GHz (4.1GHz Turbo) Socket AM3+ 95W Six-Core Desktop Processor FD6300WMHKBOX
Model #:FD6300WMHKBOX
Item #:N82E16819113286
$119.99 $119.99
G.SKILL Ripjaws Series 8GB (2 x 4GB) 240-Pin DDR3 SDRAM DDR3 1600 (PC3 12800) Desktop Memory Model F3-12800CL9D-8GBRL
Model #:F3-12800CL9D-8GBRL
Item #:N82E16820231314
$84.99 $84.99
Check around; RAM prices are high but there are deals here and there. I didn't look more closely at RAM, but I use mostly G.Skill myself.
Western Digital WD Blue WD5000AAKX 500GB 7200 RPM 16MB Cache SATA 6.0Gb/s 3.5" Internal Hard Drive Bare Drive - OEM
Model #:WD5000AAKX
Item #:N82E16822136769
$59.99 $59.99
Easy to go with 1TB, or perhaps add a SSD, but this is a good baseline.
Subtotal: $639.93
I've left some money in your budget you could use to make any number of improvements, of your choice. For example, you may wish to add a decent cooler like a Xigmatek Gaia for overclocking, or perhaps get a stronger video card (you'll need a PSU upgrade for cards needing more than one PCIe power connector), or a larger hard drive.
Hmmm, it looks like I forgot the optical drive, but that shouldn't cost more than $19-$20. Some items have shipping costs, but some also have rebates.